# Building a hybrid and dynamic mathematical space

• Mathematica
• Alvaro.Castro.Castilla@gmail.com
In summary, the conversation discusses the concept of building a "dynamic abstract space" for a digital architecture project. This space would be created by gluing together various types of spaces and would also contain particles that can dynamically reconfigure the space. The conversation also touches on potential mathematical definitions for this space and its applicability to explaining programmable objects and computer simulations.
Alvaro.Castro.Castilla@gmail.com
building a "hybrid" and dynamic mathematical space

Hello,

Maybe I'm going to say very stupid or crazy thing for real
mathematicians (I'm an architect):

I want to build a concept that I call "dynamic abstract space" ("das"
from now) for a digital architecture project. I would like to be able
to say the idea I have in mind with mathematics.

This is the essence of the idea:
1) I have a n-dimensional space (the "das") which is built from gluing
together ANY number of ANY type of spaces:
A boolea algebra, a Minkowski space, a ring, R=B3, N, C...

2) Then I introduce particles in my space which are m-dimensional
spaces. If the particles are cointained in the space, then there is no
dynamic reconfiguration of the space, but if the particles are not
contained, the space grows until is able to contain them (for example
in a R=B2 space if we want to insert a R=B3 particle, we have to expand
the space up to R=B3, in a very simple situation). That is the reason I
call it "dynamic".

How to mathematically define that space and that particles?
What do you think of explaining programmable objects and their
variables through this "spaces" and "particles"?

-----

The second thing I would ask is:
Is it correct to say that inside a computer simulation we are inside a
mathematical space of, for example:
R=B3 * R+
for a 3-d space running in a continuous time, or:
R=B3 * N
for a 3-d space running in a step by step basis.
?

THANKS for all your help!

:-)

Hello,

Thank you for sharing your idea with us. I find this concept of a "dynamic abstract space" very interesting. It seems like you are trying to create a mathematical space that is flexible and adaptable, which is a unique approach.

To answer your first question, there are several ways to mathematically define such a space. One approach could be to use topology, which is the study of properties that are preserved under continuous deformations. In this case, your "das" could be seen as a topological space, where the particles are represented as subspaces. Another approach could be to use category theory, which is a branch of mathematics that studies abstract structures and their relationships. In this case, your "das" could be seen as a category, with the particles as objects and the relationships between them as morphisms.

As for your second question, it is correct to say that a computer simulation creates a mathematical space in which the simulated objects exist. The specific mathematical space would depend on the type of simulation being run. In the examples you gave, R=B3 * R+ and R=B3 * N, the first one would represent a continuous simulation, while the second one would represent a discrete simulation.

I think your idea of using this concept to explain programmable objects and their variables is interesting. It could potentially provide a visual representation of how these objects interact and adapt in a dynamic space.

I hope this helps in your exploration of this concept. Best of luck with your digital architecture project!

Hello,

Your idea of a "dynamic abstract space" sounds very interesting and unique. It seems like you are trying to create a hybrid space that combines different mathematical concepts and allows for dynamic reconfiguration. This could be a fascinating approach in the field of digital architecture.

To mathematically define this space, you could start by defining the basic elements that make up your n-dimensional space. For example, you mentioned boolean algebra, Minkowski space, rings, and other mathematical concepts. You could then explore how these different elements can be combined and glued together to create your hybrid space.

As for the particles, it seems like you are using them as a way to introduce new elements into the space and trigger dynamic reconfiguration. You could define these particles as m-dimensional spaces and explore how they interact with the larger n-dimensional space. This could involve looking at concepts like containment, expansion, and how the particles affect the overall structure of the space.

In terms of programmable objects and their variables, it could be possible to explain them through this concept of "spaces" and "particles." For example, you could think of the programmable objects as particles that can be inserted into the larger space and their variables as the properties that affect the dynamic reconfiguration of the space.

Regarding your question about computer simulations, it is correct to say that we are inside a mathematical space when using simulations. Depending on the type of simulation and its underlying mathematical principles, the space could be represented by R=B3 * R+ or R=B3 * N, as you mentioned.

I hope this helps and provides some ideas for further exploration. Good luck with your project!

## 1. What is a hybrid and dynamic mathematical space?

A hybrid and dynamic mathematical space is a mathematical concept that combines elements from different mathematical theories or frameworks to create a more comprehensive and adaptable space. It is a way of integrating different mathematical perspectives in order to better understand and solve complex problems.

## 2. How is a hybrid and dynamic mathematical space different from a traditional mathematical space?

A traditional mathematical space is based on a single theory or framework, while a hybrid and dynamic mathematical space incorporates multiple theories or frameworks. This allows for a more flexible and robust approach to problem-solving.

## 3. What are the benefits of building a hybrid and dynamic mathematical space?

Building a hybrid and dynamic mathematical space allows for a more comprehensive understanding of complex problems by incorporating multiple perspectives. It also provides a more adaptable approach to problem-solving, as different theories or frameworks can be used depending on the specific problem at hand.

## 4. What are some real-world applications of a hybrid and dynamic mathematical space?

A hybrid and dynamic mathematical space has many potential applications, including in fields such as physics, engineering, economics, and computer science. It can be used to model and solve complex systems, optimize processes, and make predictions in a variety of industries.

## 5. How can one go about building a hybrid and dynamic mathematical space?

Building a hybrid and dynamic mathematical space requires a deep understanding of multiple mathematical theories and frameworks. It also requires creativity and critical thinking skills to determine which elements from each theory or framework are most relevant and useful for a given problem. Collaboration with other experts in different fields may also be beneficial in creating a comprehensive and effective hybrid and dynamic mathematical space.

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